THE PROBABILITY OF FIXATION OF A FAVORED ALLELE IN A SUBDIVIDED POPULATION

In a stably subdivided population with symmetric migration, the chance that a favoured allele will be fixed is independent of population str ucture. However, random extinction introduces an extra component of sa mpling drift, and reduces the probability of fixation. In this paper, the fixation probability is calculated using the diffusion approximati on; comparison with exact solution of the discrete model shows this to be accurate. The key parameters are the rates of selection, migration and extinction, scaled relative to population size (S = 4Ns, M = 4Nm, LAMBDA = 4Nlambda); results apply to a haploid model, or to diploids with additive selection. If new colonies derive from many demes, the f ixation probability cannot be reduced by more than half. However, if c olonies are initially homogeneous, fixation probability can be much re duced. In the limit of low migration and extinction rates (M, LAMBDA m uch less than 1), it is 2s/{1 + (LAMBDA/MS) (1 - exp (- S))}, whilst i n the opposite limit (M, LAMBDA much greater than 1), it is 4sM/{LAMBD A(LAMBDA + M)}. In the limit of weak selection (S much less than 1), i t is 4sM/{(LAMBDA + 2) (LAMBDA + M)}. These factors are not the same a s the reduction in effective population size (N(e)/N), showing that th e effects of population structure on selected alleles cannot be unders tood from the behaviour of neutral markers.